The Second-Order Post-Newtonian Equations Of Light Ray

The gravitational deflection of light has played an important historic role in the verification of theories of gravitation. Because of the improvement of experiment technologies, the precision of measurement is higher and higher. The previous post-Newtonian theory can only consider questions in one global coordinate system, therefore they cannot correctly calculate the relativistic contribution from multipole moments which should be calculated in the local coordinates. When dealing with questions in two or more systems, we have to use the approximation method in multiple systems梩he DSX scheme. A series of space astrometric missions are proposed recently, in these projects the second-order contribution to light propagation in multiple systems have to be considered. However, the DSX scheme is the first post-Newtonian (1PN) approximation, it was extended to the second-order contributions to light propagation newly, that is, the second-order post-Newtonian (2PN) equations of light ray have to be discussed under the recent extension of DSX scheme. In this paper, the iterative method is used to establish and calculate the 2PN equations of light ray. The 2PN equations of light ray in the solar system have been deduced from the metric tensor and Christoffel Symbols. When the terms higher than 1/c4 are neglected, the 2PN equations of light ray reduce to the 1PN equations which already appeared in some textbooks. Further, we consider the parametrized metric, there are two post-Newtonian parameters (y and B) in the relativistic celestial mechanics in 1PN. According with previous work and satisfying the requirement of experiments in the solar system, we introduce a new parameterε in the metric tensorgij. So there are three parameters (γ, β and ε) in theequations of light ray which we deduced first time. Using these equations light propagation in the solar system can be calculated to the second-order post-Newtonian precision with three parameters.